what is x if x plus 2 equals 7 (something other than 5)

Question

    

 

      lx+2l=7

Answer 1

How this answer is explained (and understood) is more important than having a correct answer.  So,

     Absolute value of x, denoted by |x|, means that either (+x) or (-x) as input produces POSITIVE(x) as output.  The absolute value function disregards the sign, but keeps the value.

 

Note:  Using computers, it is common to see this function written as ABS(x).

Thought question:  What does the expression  ( -|x| ) produce?

 

Thus, |7| means either the input could be either (+7) or (-7).  When the sign is removed, the numbers have the same magnitude (size).

 

Once the Absolute Value Bars [note: not brackets!] are removed, there are two expressions for the rest of the problem.

 

With the expression ( |x+2| ), we must now consider both ( +(x+2) ) and ( -(x+2) ) to continue solving the problem.

 

Either:      +(x+2) = 7                     or          -(x+2) = 7

                   x+2 = 7                                      -x-2 = 7                              [distribute]

                    x = 5                                          -x = 9                              [add 2 to both sides]

                                                                     x = -9                             [multiply both sides by (-1)]

 

If the answer must be "something other than x=5, then it is x=-9."   [note: in later math, this will be important (for example, when finding the length of the side of a garden, we come up with either 5 feet or -9 feet, we have a good reason to select 5 feet! )

 

More notes:

   It is mathematically correct, but it skips a step, to say that |x+2|=7 means either (x+2)=7 or (x+2)=-7  [see explanation above.]

 

Answer 2

Hi Suxiy, 

Since we are already given lx+2l=7, and you already know that x can equal five, we have: 

|5+2|=7

|7|=7

Consider: We need to remember that when calculating an absolute value, the term in the brackets could be a negative number.

We ask ourselves: What negative value of x can add to two to give us 7 as an answer?

|-9+2|=7 because |-7|=7

∴x can also equal -9.

Best, 

Star

Answer 3

When you have absolute values in an equation, you make two equations to solve since the inside of the absolute value could be positive or negative.

 

x + 2 = 7 and  x + 2 = -7

So x = 5  and x = -9